Nov 07 2011

Holmesian Deduction

Sherlock Holmes is perhaps the most iconic detective in literature. His character continues to enthrall – there is a new BBC series with a modern Sherlock Holmes, and other popular TV characters, such as House, are significantly based on Holmes. What I think is endlessly compelling about Holmes is the seemingly preternatural skill with which he “deduces” specific facts about people and situations, based upon careful observation and a rigorous thought process. But then he makes it all seem so easy in retrospect when he reveals his method.

Because Holmes is such a fascinating character and Doyle wrote prolifically about this character, Holmes is also a useful and frequently used example of logic and the process of detective work. I took a course on Holmes in medical school, using Sherlock Holmes short stories as examples of diagnostic principles (Arthur Conan Doyle was a physician, and clearly drew upon this experience in writing Holmes). A recent Scientific American article, for example, used Holmesian logic as an example of how not to make several common fallacies of thinking – falling for the conjunction fallacy, the representativeness heuristic, and failure to consider the base-rate.

Briefly, we tend to assume that someone belongs to a category if they have features we find representative of that category, or if we can readily bring to mind similar examples. We tend not to consider the base rate – what percentage of the relevant population belongs to that category. Sherlock Holmes encapsulated part of this idea with his famous quip to Watson that if you hear clopping on a cobblestone street in London, think horse, not zebra. This principle is common in medical diagnosis, and in fact we call rare diseases (those with a low base-rate) “zebras” after Holmes’ example. In other words – even if a person has signs and symptoms that resemble a specific disease, the probability of that diagnosis is still low if the base rate is very low – it’s a rare disease. In fact, an atypical presentation of a very common disease may be more likely than a typical presentation of a rare disease.

But we tend to be more compelled by the representativeness of a person or situation than the base rate. Our evolved innate calculations of probability are flawed in this way.

The article also discusses the conjunction fallacy – the tendency to think that two likely conclusions are more likely that either alone. Mathematically, this cannot be true – the probability of A+B must be less than the probability of either A or B. This is easy enough to understand, but we tend to ignore this when confronted with a representative example. For example, if I describe for you a typical nerd and ask about the probability that they work in IT and play video games, your naive logic tells you that the probability of both is greater than the probability of either by itself, because they are both representative of the typical nerd.

Holmes is able to arrive at such accurate statements about those he observes partly because he does not fall for all the typical fallacies and heuristics that hamper our thinking. When they are explained, they make perfect logical sense. The average person, however, is typically not aware of all the flaws in logic that plague our thinking day to day.

However, I have to point out that the process that Sherlock Holmes engages in is usually not deduction, even though that is the term the character Holmes uses to describe his process. The new BBC Holmes series, for example, has a website called The Science of Deduction (which exists also in the world of the series as Holmes’ website).

Deduction is the logical process of going from the general to the specific. If one or more premises – general statements about the world – are true, then a specific conclusion must also be true. This is deduction. The textbook example of this is: Premise 1: All men are mortal; Premise 2: Socrates is a man; Conclusion: Socrates is mortal.

There are times when Holmes does indeed use deduction, but not when he is coming to conclusions based upon his careful observations. Some logicians have referred to what Sherlock Holmes does as “Holmesian deduction” to distinguish it from deduction itself. What Holmes is largely doing is well-informed inference. He begins with careful observation of details. He then uses base rate knowledge (rather than superficial representativeness thinking) to make specific high probability guesses. Watson, he observes, has a tan. He did not get the tan in London, so he must have recently arrived from a tropical location. He puts this together with other bits of information to infer that Watson probably served in Afghanistan.

Holmes also uses a great deal of inductive knowledge. Induction is the process of going from the specific to the general – which is mostly what scientific investigation involves. We might note that every swan observed is white, and induce the general principle that all swans are white. While deductive conclusions must be true, inductive conclusions are tentative – they are extrapolations from limited data. They are also falsifiable (at least in principle) as was demonstrated by the discovery of black swans in Australia. Holmes develops general principles from inductive processes (science) and then applies them to his inferences. He spends much of his time between cases doing detailed analyses of cigar ash and other such things, providing knowledge he can then use in his investigations.

In many ways what Holmes does is very similar to the cold reading of fake psychics and real mentalists. A skilled cold reader will be armed with knowledge of the base rate of many things, such as male and female names. They will use observation and feedback in order to feed the process with information, and then make inferences about what is likely to be true. Just as with Holmes, they have the ability to amaze their target, seemingly pulling very specific information out of thin air. But just like Holmes, they are really just using a process of observation and inference.

Regardless of the purpose (medical diagnosis, entertainment, investigation, or fraud) what the character Holmes does aptly demonstrate is the power of substituting rigorous logical methodology for the naive reasoning that humans evolved.

16 responses so far

16 Responses to “Holmesian Deduction”

  1. CWon 07 Nov 2011 at 8:29 am

    You mentioned that Scientific American article, and so I thought I would point out that the author, Maria Konnikova, has been writing a series of SciAm articles that refer to Sherlock Holmes.

    “Lessons from Sherlock Holmes: From Perspective-Taking to Empathy”

    “Lessons from Sherlock Holmes: From Perspective-Taking to Empathy”

    “Lessons from Sherlock Holmes: Don’t Judge a Man by His Face”

    “Lessons from Sherlock Holmes: Trust in The Facts, Not Your Version of Them”

  2. starskepticon 07 Nov 2011 at 9:55 am

    a plaque on both your houses…

  3. locutusbrgon 07 Nov 2011 at 10:39 am

    Interesting Course.
    I have read Holmes as many people have. What always bothered me about his deductions is that the reader is left with the authors description of the event. Later I would often think that some of his Holmesian deductions would not have been so astonishing if you had the ability to be there in person. The limited view the author writes frames your ability to make the deduction. Two stories jump to mind, The red headed league, and the speckled band. If you analyze them you may find, like I did, that the author has performed a little trickery to give the impression that this was a miraculous evaluation by Holmes.
    It is kind of like the limited camera view in a horror movie. The victim is startled, when suddenly an attack occurs from an attacker that is out of view/off camera. I would think to myself, how can the victim not see a 7 foot tall hockey masked guy coming right at her across an open field a 100 yards off.
    Sometimes Doyle would do the literary equivalent.

  4. Skepticoon 07 Nov 2011 at 10:51 am

    What do you think about Holmes’s “When you have eliminated the impossible, whatever remains, however improbable, must be the truth”? It always struck me that this is flawed reasoning since you can never know all other options, and you can never know they are impossible. Isn’t it just a version of argument from ignorance? Or maybe it’s a false dilemma?

    Of course, Holmes’s creator believed in fairies, so perhaps we shouldn’t be too surprised.

  5. delaneypaon 07 Nov 2011 at 11:13 am

    @Skeptico – Yes, I have always been irked by that line, too. It is the reasoning used in the UFO community.

  6. cwfongon 07 Nov 2011 at 12:13 pm

    The form of logic used by Holmes was most commonly “abduction.”

  7. Steven Novellaon 07 Nov 2011 at 12:24 pm

    The line about eliminating the impossible is reasonable, as far as it goes. But it is limited by the factors you point out – the conclusions are only as good as the premises, that one or more options are truly impossible, and that there are no other option.

    If I recall, the times it is used by Holmes were reasonable – some options are truly impossible or can be eliminated by specific evidence, there were finite logical options available.

  8. Steven Novellaon 07 Nov 2011 at 12:31 pm

    I agree that abduction is what Holmes often does – but that is just another term for intelligent inference, the process I described above.

    In fact, Holmes goes beyond abduction. He uses abduction or inference to generate hypotheses, which he then tests with further observation. He then reveals his chain of reason, which is really hypothesis testing.

  9. neilgrahamon 07 Nov 2011 at 10:39 pm

    I am a little surprised that the blog of such an eminent skeptic would laud the work of the spiritualist, Conan Doyle. I have often thought that the spiritual aspect of Doyle was a balancing counter to his focus on rationality in the Holmes novels – obviously he found reason and logic based on empirical fact insufficiently satisfying. I know I am asking for trouble on this site when I put the view that it was a shame that his nonsecular energy was directed towards spiritualism rather than spirituality.

  10. DLCon 08 Nov 2011 at 6:38 am

    neilgraham : Conan Doyle was also not so hot as a physician, detective or bee-keeper. So ?
    do personal shortcomings invalidate the entire volume of someone’s work ? Ernest Hemingway was a womanizing alcoholic who suffered from depression and eventually blew his own brains out — does that mean we should throw “The Sun Also Rises” and “For Whom the Bell Tolls” out the window ?

    Isaac Asimov once wrote an essay for the now-defunct “Science Digest” magazine in which he detailed many of Conan Doyle’s errors — holes in Doyle’s knowledge of contemporary science which leak into Holmes’ knowledge. It’s amusing to read, even if it pokes fun at one of my favorite literary figures.

  11. Steven Novellaon 08 Nov 2011 at 8:47 am

    The contrast between Doyle and Holmes is fascinating. I have read that Doyle did not like the character of Holmes, who was a hyperrational ass in his eyes. He was surprised at the popularity of the character, which is partly why he killed him off, and then was surprised at the public outcry and relented and brought him back.

    I do think it shows that you can understand the mechanics of logic and reason and still not apply them to your personal beliefs.

  12. jhson 08 Nov 2011 at 10:54 am

    Excellent article! A quick notation correction: Your arithmetical statement about the probability of A and B is saying the opposite as your English statement. (Notice that if you read it as a simple assertion about arithmetic, it comes out false.)

    In probability, addition is “or”, and multiplication is “and”. Probabilities are between 0 and 1. Generally, multiplication makes values smaller (less likely) and addition makes them larger (more likely).

    Perhaps you wrote it that way to avoid opacity or arcaneness, but to anybody who took high school statistics, it is a grating sentence to read.

    Consider saying, “The probability of A x B (both A and also B) must be less than A + B (either A or B).” Or perhaps, omit the jargon: “The probability of both A and also B occurring must be less than either A or B occuring.”

  13. ChrisHon 08 Nov 2011 at 12:25 pm

    Dr. Novella:

    I do think it shows that you can understand the mechanics of logic and reason and still not apply them to your personal beliefs.

    Especially as they change over time. This is something that can be seen in the Professor Challenger stories.

    The first two are okay, but the last ones starting with The Land of Mist went too far into spirituality. I read somewhere that it was a reaction to the death of his son and other relatives in WWI. Sometimes grief does shadow reason.

  14. DLCon 08 Nov 2011 at 2:58 pm

    Oddly, we owe Holmes’ resurrection to an American, who was such a fan of the series that he offered Conan Doyle a hundred thousand USD to bring back the character, with the stipulation that Holmes had somehow survived his encounter with Moriarty. Soon thereafter came The Adventure of the Empty House.
    Learning how to rule out the impossible is good. but first you have to learn how to discern the impossible from the improbable. By impossible, I mean “could not have happened within the specified area during the specified time frame.”

  15. VRAlbanyon 08 Nov 2011 at 8:15 pm

    “It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.”

    That one always stuck with me, and it applies to so many controversies we see in the news today and that are dealt with on this blog.

  16. Bronze Dogon 13 Nov 2011 at 2:23 pm

    I was also bugged by the “eliminating the impossible” line in general context, especially in line with Doyle’s spiritualism. I remember something about Doyle trying to argue that Houdini did one of his escape tricks by dematerializing and rematerializing outside the box, and thinking of how that line of logic might have been used to rationalize crazy scenarios. Something along the lines of, “He couldn’t unlock that padlock, therefore he must be using magic.” when Houdini might have had something like a false bottom in the container, a lockpick hidden in his mouth, or whatever.

    This, however, is something I hadn’t heard about:

    The contrast between Doyle and Holmes is fascinating. I have read that Doyle did not like the character of Holmes, who was a hyperrational ass in his eyes. He was surprised at the popularity of the character, which is partly why he killed him off, and then was surprised at the public outcry and relented and brought him back.

    I do think it shows that you can understand the mechanics of logic and reason and still not apply them to your personal beliefs.

    I agree that it’s interesting, and certainly seems like a reasonable explanation to me.

    Back to the quote about eliminating the impossible, one thing I bear in mind as an extension: If you eliminate all the hypotheses you generated as impossible, that’s usually a good time to start examining and challenging the assumptions you’ve been working under.

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